To conduct high-precision and high-resolution numerical simulation of complex flow structures in turbomachinery, a high-order finite volume weighted essentially non-oscillatory (WENO) scheme for the large eddy simulation (LES) is improved and embedded into the three-dimensional viscous unsteady CFD solver NUAA-Turbo. Firstly, the spectral characteristics and unsteady convergence of the improved WENO scheme are studied. Compared with the classical WENO scheme, the improved WENO scheme has better dissipation and dispersion characteristics and faster convergence speed. Then, the coefficient CW of the Wall-Adapting Local Eddy-viscosity (WALE) model is calibrated by decaying homogeneous isotropic turbulence (DHIT) test case. Finally, the scheme is applied to conduct high-precision LES calculations of turbulent boundary layer flow, supersonic compression corner flow, and low-pressure turbine cascade separation flow. The numerical simulation results show that this WENO scheme has excellent shock wave capture ability and turbulence resolution and can capture more flow field details with less mesh size, greatly reducing the computational cost and laying a foundation for large-scale engineering application of LES.

In this paper, we propose an efficient numerical method to solve the diffusive logistic model with a free boundary which is often used to simulate the spreading of the new or invasive species. The boundary movement is tracked by the level-set method, where the Hamilton-Jacobi weighted essentially nonoscillatory (HJ-WENO) scheme is utilized to capture the boundary curve embedded by the Cartesian grids via the embedded boundary method. Then the radial basis function-finite difference (RBF-FD) method is adopted to the spatial discretization and the IMEX scheme is considered for time integration. A variety of numerical examples are carried out to demonstrate the evolution of diffusive logistic model in different initial boundaries.

The aim of this work is to introduce a mathematical model representing the evolution of the temperature in a vegetation cover and the ground underneath it. Vegetation, and its interaction with soil, plays a very important role in the protection of soil surface from the action of sun and precipitations. A reduction in the vegetated mass increase the risk of desertification, soil erosion or surface runoffs which which can give rise to soil loss and sediment retention. These processes can favour climate change and global warming, which are major concerns nowadays. The mathematical model presented takes into account the main processes involved in vegetation cover and the interaction with the soil, among which, we can mention the Leaf Area Index, which is a dimensionless quantity defined as the one-sided green leaf area per unit ground surface area, or albedo and co-albedo which are clearly influenced by the vegetation. It is also considered a nonlinear heat capacity in the soil which incorporates the latent heat of fusion, when the phase change takes place. The numerical technique used to solve the mathematical model is based on a finite volume scheme with Weighted Essentially Non Oscillatory technique for spatial reconstruction and the third order Runge-Kutta Total Variation Diminishing numerical scheme is used for time integration. Some numerical examples are solved to obtain the distribution of temperature both in the vegetation cover and the soil.

This work deals with a numerical implementation of a fifth order CENTRAL WENO-TVD (\textit{Weighted Essentially Non-Oscillatory-Total Variation Dimimishing}) of Haschem (2006) scheme applied to the convective terms of some hyperbolic conservation laws problems, in a volume finite framework. The WENO-TVD scheme is used to solve the 1D advection and Burgers equations. For this case is implemented two different numerical fluxes: The Lax-Friedrichs and TVD fluxes. In the TVD fluxes the schemes applied are in flux-limiter form. The schemes implemented for this flux are: Van Albada-1 (van Albada et al.,1982), van Albada-2 (Kermani et al., 2003), van Leer (Hassanzadeh, 2009) and MINMOD (Hirsch, 2007). The WENO type schemes are characterized for their high order approximation, and do not produce spurious oscilations near discontinuities, shocks and higher gradients. A third order Runge-Kutta TVD for the temporal variable is used. Qualitative and quantitative comparison are presented. The numerical solutions are computed with an in-house computer code developed in MATLAB software. In future works, it will develope a paralelization of computer code for solving systems of conservation laws, e.g. Euler equations of gas dynamics.